Can non-US citizens with no US residence or citizenship open up a checking/savings account at any major US banks such as Capital One or HYS?

Sorry type on my title I meant SAVINGS I do have a checkings! Hello! I am wondering if an 18+ year old who is not yet a citizen or legal resident of the US can open a savings account with a bank who will actually grown money such as Capital One or a high yield savings account. Does anyone have experience with this? Wealthfront seemed like a good option until they required proof of US citizenship. Thanks!